For nonvolatile memories such as flash memories and phase-change memories, endurance and reliability are both important challenges. Write-Efficient Memory (WEM) is an important rewriting model to solve the endurance problem. An optimal rewriting code has been proposed to approach the rewriting capacity of WEM. Aiming at jointly solving the endurance and the data reliability problem, this work focuses on a combined error correction and rewriting code for WEM. To that end, a new coding model,

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... y WEM, is proposed here. Its noisy rewriting capacity is explored. An efficient coding scheme is constructed for a special case of noisy WEM. Its decoding and rewriting operations can be done in time O(N log N ), with N as the length of the codeword, and it provides a lower bound to the noisy WEM's capacity.